The story starts in the middle of the 20th century. "Schwartz" has just retired and is happy facing the rest of a joyful life, when suddenly he is transferred 20000 (<- no mistake) years into the future. (Which of course he doesn't understand at first).
Earth has become radioactive and the inhabitants are the outcasts of the galaxy, even if there is this totally unprobable theory that it is the original source of humanity.
Because of the scarce resources earth has the regulation that everyone older than sixty has to be removed (killed!). And of course just _everyone_ complies to this out of his "free" will... (<- sarcasm) and Schwartz is older than 60.
This scenario is the layout for a complex plot in which the population of Earth tries to destroy the rest of humanity, and of course Schwartz gets entangled in this conspiracy and the saving of the galaxy.
Well... That was about 1/4 of the content of the book, and only _one_ track of the story (there are at least two others and all tracks are so closely connected that you can't really break them apart).
I believe it's almost impossible to really summarize the story, because this book is written in a kind of compressed mode (it is in fact quite short), each page reveals another unknown, and unforeseen part of the story - it simply takes your breath away.
It is my most favourite book of Asimov (and I claim that I know almost everything he wrote), even if it's not very famous. It contains everything: mystery, conspiracy, love story (<- yes it's not in my summary, but it is in the book :-) ), science fiction, an intriguing scocial scenario,... just everything!
It is one the "Imperial" (<- that's what I call them) novels, which are set in the high time of the "Imperium of Trantor". There are two other stories in this setting: "The Currents of Space" and "Stars like Sust". All three novels are completely independent of the rest of his books (which is probably a reason why they are not as famous), and are not connected to each other.
Unfortunately it is almost impossible to get a copy of the book :-(. I made the mistake to lent it to someone and it never came back... Since then I try to get this book again, but without success...